# In the limit that all the binding sites are saturated with ligand?

Consider a single domain protein which has two conformations A and B in equilibrium with constant Show more Consider a single domain protein which has two conformations A and B in equilibrium with constant L. The protein has two binding sites for two different ligands. In conformation A the protein binds ligand X with affinity KA and/or ligand Y also with affinity KA. The two binding events do not interact in conformation A. The B conformation binds the two ligands cooperatively in an all or none fashion with affinity KB. That is the only ligation states for conformation B are no ligands bound or both ligands bound. (a) Write an expression for the sum over all possible ligation and conformational states of the protein. Express all terms containing [B] in terms of [A] and L so that you can factor out [A]. Now formulate an expression for fB/fA the fraction of protein in the B conformation relative to the fraction in A in terms of KA KB x y and L. (b) Now assume that the two ligands are actually identical. In this case what is fB/fA at x = 0? In the limit that all the binding sites are saturated with ligand? What value of x maximizes the fraction of the protein that is in the A conformation and what is fB/fA at this ligand concentration? (c) Sketch fB/fA as a function of the ligand concentration x. Indicate on the graph all the values that you computed in Part B. Show less

### QUICK QUOTE

Approximately 250 words
\$12